a portfolio model of capital flows to emerging markets

Journal of Development Economics 89 (2009) 181–193

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Journal of Development Economics

j ourna l homepage: www.e lsev ie r.com/ locate /econbase

A portfolio model of capital flows to emerging markets☆

Michael B. Devereux a,⁎, Alan Sutherland b

a CEPR and Department of Economics, University of British Columbia, Canadab CEPR and School of Economics and Finance, University of St Andrews, UK

☆ Prepared for the IMF conference “New PerspectiveApril 2007. We thank the editors, an anonymous refereeat the conference for comments on an earlier draft. Suppand Finance Programme, award 156-25-0027. DevereuCanada, and the Royal Bank of Canada for financial suppthose of the authors, and do not reflect the position of t⁎ Corresponding author.

E-mail addresses: [email protected] (M.B. D(A. Sutherland).

URL's: http://www.econ.ubc.ca/devereux/mdeverehttp://www.st-and.ac.uk/~ajs10/home.html (A. Suther

0304-3878/$ – see front matter © 2008 Elsevier B.V. Adoi:10.1016/j.jdeveco.2008.07.002

a b s t r a c t
a r t i c l e i n f o
Article history:
Since the crises of the late Received 5 June 2007Received in revised form 11 June 2008Accepted 14 July 2008
JEL classification:E52E58F41

Keywords:Country portfoliosEmerging markets

1990's, most emerging market economies have built up substantial positiveholdings of US dollar treasury bills, while at the same time experiencing a boom in FDI capital inflows. Thispaper develops a DSGE model of the interaction between an emerging market economy and an advancedeconomy which incorporates two-way capital flows between the economies. The novel aspect of the paper isto make use of new methods for analyzing portfolio choice in DSGE models. We compare a range ofalternative financial market structures, in each case computing equilibrium portfolios. We find that anasymmetric configuration where the emerging economy holds nominal bonds and issues claims on capital(FDI) can achieve a considerable degree of international risk-sharing. This risk-sharing can be enhanced by amore stable monetary policy in the advanced economy.

© 2008 Elsevier B.V. All rights reserved.

1. Introduction

In the decade since the crises of the 1990's, the internationalfinancial landscape has evolved and changed in ways that fewobservers would have predicted at that time. Emerging economieshave generally experienced strong and uninterrupted economicgrowth with no major crises. Capital flows from industrial countriesin the form of FDI, as well as portfolio and bond investment, have beenstrong. Sovereign spreads have been low by historic standards for anumber of years. For most emerging countries, external accounts haveswung sharply from positions of net deficits in the mid-1990's togenerally strong surpluses at present. In addition, these countries haveeliminated their financial vulnerabilities, displayed so clearly duringthe crisis years, by correcting the currency and maturity mismatchesin their national balance sheets. Some countries have abandoned tightexchange rate pegs and moved towards flexible inflation targeting.

s on Financial Globalization”,, Martin Evans and participantsorted by ESRC World Economyx thanks SSHRC, the Bank ofort. The views here are solelyhe Bank of Canada.

evereux), [email protected]

ux.htm (M.B. Devereux),land).

ll rights reserved.

More generally, the quality of policy-making in the fiscal and financialdomain has improved greatly.

There is no single explanation for this surplus of good economicnews from the emerging markets. High global saving has led to aprolonged period of low real interest rates, reducing the potential forcrises. The build-up of strong positive net external positions as well aslarge stocks of foreign exchange rate reserves has had the same effect,andmore generally has instilled a strong confidence in the investmentpotential of emerging economies. But in addition, real economicgrowth has been stimulated by high demand for exports from theindustrial world (in particular the US), and commodity prices boomshave generated huge net gains for many emerging countries.

One general feature of emerging economies' recent experience,that differs from previous episodes of high capital inflows andeconomic growth, is the degree to which they have been participantsin the globalization of financial markets. Rather than simply beingrecipients of net capital inflows or generators of outflows, manyemerging countries have displayed growth in gross external financialassets and liabilities that are much larger than net positions. In thissense, their experience mirrors that of many advanced economies, asdocumented in the seminal work of Lane and Milesi-Ferretti (2001,2005, 2006). While most recent discussion of global imbalances hasfocused on the size of net external surpluses of China and otheremerging economies, indicating the apparently perverse situation ofcapital outflows from the developing world to developed economies(or more accurately, the US), in the background there is a largedegree of two way capital flow. Emerging economies have beenaccumulating large stocks of US treasury bills going into officialreserve assets, but they have also been receiving large inflows of FDI

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182 M.B. Devereux, A. Sutherland / Journal of Development Economics 89 (2009) 181–193

and portfolio equity investment, as well as private bond marketinflows. Lane and Milesi-Ferretti (2006) document this turnaroundin the portfolio position of emerging market economies taken as awhole. From the situation in the mid 1990's, where many of theseeconomies were substantial net debtors in non-contingent assetssuch as bank loans and short term US dollar bonds, now they havesubstantial net positive positions in fixed income assets, while beingon the whole net debtors in FDI and portfolio equity investment.There is an argument that this is in fact a muchmore efficient form offinancing development lending for emerging market economies, interms of achieving the most desired degree of international risksharing.

This paper analyses the impact of financial globalization inemerging market economies, paying particular attention to thedeterminants of country portfolio positions. We explore the factorsunderlying the determinants of an optimal risk-sharing portfolio foran emerging market economy and an advanced economy. Theemerging economy is characterized by a high country-specificproductivity risk. We explore how international risk-sharing can beachieved under a number of alternative financial market configura-tions, ranging from a situation of no financial markets (i.e. noportfolio diversification) to one of complete markets. Of particularinterest is an intermediate financial structure, where there isinternational trade in equity-FDI claims of the emerging economyas well as nominal bonds denominated in the currency of theadvanced economy. This is meant in a general sense to represent thepresent structure of twoway capital flows between emergingmarketeconomies and the advanced economies as described in the previousparagraph.

For each financial market configuration, we compute the equili-brium optimal portfolio positions of each economy, given the financialinstruments available, as well as the nature of country specific risks.Our analysis is built around a dynamic stochastic general equilibrium(DSGE) model of the interaction between an emerging marketeconomy and the rest of the world. However, unlike the standardDSGE framework, we are able to incorporate two-way capital flowsacross countries. We do this by making use of new developments inthe study of portfolio choice in general equilibrium environments (seeDevereux and Sutherland, 2006, 2007), in order to isolate thedeterminants of gross portfolio positions for an emerging marketeconomy.1

Our results indicate that financial globalization, wherein anemerging market economy may simultaneously build up positivegross positions in non-contingent international bond assets, andnegative positions in FDI and portfolio equity, may offer a considerableenhancement of international risk-sharing, relative to a case whereonly one-way intertemporal capital flows can take place. Never-theless, we find that this financial structure is unable to attain acomplete-markets full risk-sharing equilibrium. In our model, such anallocation can be attained if there is unrestricted trade in bothcountry's equities and a non-contingent real bond.

The degree of risk-sharing attained with two way capital flowsdepends on some key features of the model. In particular, becauseagents engage in risk-sharing using nominal home currency bonds,the amount of price volatility will affect risk-sharing, even though allnominal prices are flexible. In particular, more volatility arising fromprice shocks will reduce the size of optimal portfolios, and reduce risk-sharing across countries.

We compare the response to productivity shocks under alter-native asset market configurations. Optimal portfolio diversification

1 See also Engel and Matsumoto (2005), Evans and Hnatkovska (2005), Kollmann(2006), and Tille and vanWincoop (2007) among other papers, for recent contributionsto the literature on portfolio choice in general equilibrium.

tends to reduce the gap between the overall consumption responsesto shocks, but at the same time tends to increase the movement inthe net asset position. Because we can compute the optimal port-folio structure for each country, we can also decompose the changein net assets into the separate movement in gross liabilities(nominal bonds) and gross assets (FDI equity). In some cases,gross assets and liabilities tend to move in opposite directions, whilein other cases they move in the same direction. Finally, we can breakdown the overall movement in gross portfolios (or capital flows),into price, (or valuation) effects, andquantity (or portfolio re-balancing)effects.

The rest of the paper is organized as follows. The next sectiondiscusses some recent developments in financial markets and countryportfolios for emerging markets. Section 3 sets out the two countrydynamic model, and explains the method of constructing optimalportfolios. Section 4 discusses the general method of portfolio com-putation. Section 5 presents themain results of themodel for portfoliochoice, risk-sharing, and international capital flows. Some conclusionsthen follow.

2. Evidence

In this section we review some recent experience of the externalbalance and portfolio structure of developing and emerging marketeconomies. The growing current account surpluses of emergingmarket economies, and in particular the Asian economies, is thecounterpart in large degree to the increase in the US current accountdeficit. For many emerging countries, these current account surplusesdate back to the crises of the late 1990's.

The model we analyze below highlights the importance ofportfolio structure and the evolution of gross asset and liabilitypositions. Nevertheless, we begin by focusing on the experience ofnet foreign assets. Fig. 1 describes the evolution of the net foreigndebt to GDP ratio for 76 (non oil-exporting) developing andemerging market economies over the period 1990–2004, wherethe data are obtained from the Lane and Milesi-Ferretti (2006)‘External Wealth of Nations’ (EWN) data-set. The most strikingaspect of Fig. 1 is the sharp turnaround in the net foreign debt ratioimmediately after the Asian crisis. The ratio grew sharply from themid-1990's onwards, moving from about 35% to 48% between 1995and 1999. But it fell quickly from this peak, and at the end of thesample (2004) had returned to its mid-1990's level. Although theEWN data set includes valuation effects of exchange rates and assetprices on gross assets and liabilities in order to construct the net debtmeasure, this rapid improvement reflects primarily the turnaroundin the current accounts of emerging market economies from deficitto surplus following the Asian crisis.

A central reason to analyze the determinants of gross exter-nal positions is the phenomenon of ‘financial globalization’, or the

Fig. 1. Developing and emerging market countries.

Fig. 3. Equity and FDI liabilities.

Fig. 4. Debt assets and foreign exchange reserves.

Fig. 2. Gross portfolios.

183M.B. Devereux, A. Sutherland / Journal of Development Economics 89 (2009) 181–193

simultaneous increase in stocks of gross external assets andliabilities. It is well-recognized that advanced economies have ex-perienced rapid increases in gross external positions over the lastdecade. To what extent is this also true of developing economies?The top panel of Fig. 2 illustrates the movement of gross externalassets and liabilities, relative to GDP, for the same sample ofcountries as in Fig. 1, over the 1990–2004 period. This confirmsthat on average developing countries are net debtors, as shown inFig. 1. But gross assets and liabilities both grew considerably over theperiod. In particular, average gross assets doubled from 34 to 68% ofGDP over the period.

The lower panels of Fig. 2 show gross asset and liability positionsfor China and India, the two emerging economy ‘giants’. In both cases,we see a strong trend in the growth of both gross assets and liabilities.For China, the increase in gross assets was fast enough to turn it into anet creditor at the end of the sample. At the beginning of the sample,India is essentially in financial autarky, with very low ratios of grossassets and liabilities to GDP. But both series increase dramatically overthe subsequent 15 years.

It is not just the presence of large gross external positions that isimportant, but also the composition of these assets and liabilities. Akey implication of the model analyzed below is that emerging marketcountries participate in cross country risk-sharing through theaccumulation of debt asset claims on advanced economies, whileissuing claims in the form of equity and FDI liabilities that are held byresidents of advanced economies. Lane and Milesi-Ferretti (2006)note that this dichotomy in portfolio composition is seen increasinglyin the data over the last decade. The top panels of Figs. 3 and 4 confirmthis for the same group of developing and emerging market countriesas before. Over the sample, the equity liabilities-GDP ratio increases

2 In principle, of course, it would be desirable to allow for the market structure to bedetermined endogenously. In the case of China, it might be argued that the presence ofcapital controls provides a direct explanation for the portfolio configuration wherebyFDI is financed by positive holdings of rest-of-world bonds. But more generally, it isimportant to consider why the restricted range of asset holdings that are allowed inthe EB configuration might arise as a result of differences across countries in transactionscosts, financial market distortions, or informational asymmetries. Two factors mightbe important in this consideration. First, as will be shown below, holding homecountry nominal bonds acts as a relatively efficient claim on home output, and so isa (imperfect) substitute for holding home equity. But if we allow for unrestricted tradein both countries equities, and nominal bonds, then markets would be complete(see Section 5.4 below), and agents in the foreign country will take a large holding indomestic equity. However, if wewere to introduce additional transactions costs to foreignagents holding of home equity, then agents in the foreign country would have a biastowards home bonds, and away from home equity. That is, it is possible to obtain aconfiguration which is close to the EB outcome in the presence of transactions costs ofholding equity. A second possible explanation of the EB configuration may be developedalong the lines of Mendoza et al. (2007). They show that, if different countries havedifferent contract enforcement technologies, then residents of the country with betterenforcement may take a long portfolio position in risky assets of the other country,financed partially by a negative position in risk-free bonds. This describes an outcomesimilar to our EB configuration.


four-fold. At the same time the ratio of debt assets to GDP increasesfrom 32 to 52%. If we restrict our focus solely to foreign exchange ratereserves to GDP, the increase is more dramatic, going from 7% of GDPin 1990 to 21% in 2004.

The lower panels of Figs. 3 and 4 confirm the same trends for Chinaand India. In fact, the movements are much more pronounced forthese two cases. In particular, China's equity liabilities to GDP ratioincreased six-fold over the sample, and its debt assets to GDP ratioincreased almost three-fold. Notably, foreign exchange reservesincrease quite sharply towards the end of the sample. Again, India'sgrowth begins from a very low base, but we see a substantial increasein FDI liabilities, as well as debt assets and foreign exchange ratereserves.

While these figures scale the portfolio positions to overall GDP, asimilar picture appears if we scale by the gross liability and assetstocks. In particular, for the overall country sample, as well as forChina and India, there is a trend towards an increase in the share ofliabilities in equity and FDI, and a trend towards an increase in theshare of gross assets in debt instruments, and in particular inforeign exchange rate reserves. Hence, there is clear evidence notjust of an increase in globalization for developing and emergingmarket economies, but also of a movement in portfolio compo-sition. In the next section we examine the risk-sharing impli-cations of these portfolio trends in a dynamic general equilibriumenvironment.

3. The model

The model is based on a standard two-country version of the neo-classical growth model. There is a single world good which isproduced by labor and capital in each country. Labor is immobileacross countries, but there is no impediment to movement of goods.We think of the home country as being ‘developed’, and the foreigncountry as being ‘developing’. In the context of the model, thisdistinction is mainly captured by two features. The first is technolo-gical. The home country has a lower volatility of GDP (or moreprecisely, a lower variance of productivity shocks). The seconddistinction between the countries relates to the configuration ofassets markets. It is assumed that only home currency bonds areacceptable in international capital markets. This assumption is meantto capture the widely observed phenomenon that, at least up untilrecently, US dollar bonds dominated international capital flows, andmore particularly that emerging market currency bonds are almostnon-existent in international bond trade.

We will look at the implications for risk-sharing and capital flowsof three different financial market arrangements. In the first, weassume no possibility of portfolio diversification at all. In thisconfiguration all capital flows between the two countries can befinanced only with a non state-contingent risk-free real bond. In thiscase, there is no distinction between gross and net foreign assets, orbetween gross and net capital flows. We denote this as the NP (‘noportfolio’) model. In the second configuration, we assume anasymmetric structure, based in a broad sense on the trend ofemerging market portfolios discussed in the previous section. Underthis arrangement, there are two assets traded between the countries;equity claims on the foreign country (if the home country takes apositive foreign equity position, we think of this as FDI investment),and home-currency denominated nominal bonds (which can bethought of as representing foreign exchange reserves, or moregenerally bond assets). This offers a more enhanced set of optionsfor sharing risk, since equity returns will reflect productivity shocks inthe foreign country, but also because real returns on home currencynominal bond will be affected by exchange rate movements (orequivalently, by movements in the home currency price level).Nevertheless, we find that in general, this does not allow for fullrisk-sharing. We denote this as the EB (‘equity-bond’), model.

Finally, we look at a symmetric case, where the equities of bothcountries and a non-contingent real bondmay be traded freely amonghome and foreign residents. In this model, we find that this financialstructure is enough fully to exploit all gains from risk-sharing, andhence this represents complete markets. We denote this as the EQ(‘equity’) model.

This paper takes as given the financial market structure. The novelfocus of the analysis is to explore the degree towhich the intermediatefinancial arrangement (EB) falls between the two extremes ofportfolio autarky (NP) and complete markets (EQ)2.

3.1. Household choices

Households in each country receive wage income and asset income.In the NP model, the household can hold only a non-contingent realbond. Under this arrangement, the budget constraint for home countryhouseholds may be defined as,

Ct + qrtBt = WtHt + Dt + Bt−1; ð1Þ

where C is home consumption, B is the holding of the real bond, qris the price of the bond, and WH is wage income, with W being thereal wage, and H labor supply. D represents dividend incomereceived from the home firm. Since in this case, equity is non-traded, all dividend income from home firms is received directly bythe home country household. Note that a unit of the bond purchasedin period t−1 is assumed to pay a unit of the consumption good inperiod t.

In the EB model, the home country budget constraint is written toallow for holdings of both nominal bonds and foreign equity. Thus, wehave:

Ct + q⁎ktSft + qbtBht = WtHt + Dt + DTt + qTkt

� �Sft−1 +

Bht−1

Ptð2Þ

where qk and qb are respectively the price of foreign equity (or FDI)and the price of the home-currency nominal bond, Sf representsthe home country holdings of foreign equity, and D represents thedividend payment on equity. We let Sf be of either sign, as thedeveloped country residents may hold long or short positions on theemerging market firm. Bh is holdings of the nominal bond, whichagain may be of either sign, and P is the home country price level. Aunit of the bond purchased in period t−1 is assumed to pay a unit of


the home currency in period t. As in the NP case, in this financialarrangement, the home country still holds 100% of domestic equity3.

In the EQ model, with symmetric trade in both equities and a realbond, the home country budget constraint may be written as

Ct + q⁎ktSft + qktSht + qrtBt = WtHt + Dt + qktð ÞSht−1

+ D⁎t + qkt

� �Sht−1 + Bt−1

ð3Þ

whereqk is the price of home equity, and Sh is the home residents’ share ofthe home firm.We may re-write either Eqs. (2) or (3) in terms of netforeign assets. In the case of Eq. (2), net foreign assets may be writtenas NFAt=qkt⁎ Sft+qbtBht, while for the Eq. (3) case, we have NFAt=qkt⁎ Sft+qkt(Sht−1)+qrtBt. Then we may re-write Eq. (2) as follows

Ct + NFAt = WtHt + Dt + rxtαt−1 + rbtNFAt−1 ð4Þ

Hereαt−1=qkt−1⁎ Sft−1 is the real holding of equity, and rxt=rkt⁎−rbtrepresents the excess return on equity relative to debt, where rkt⁎=(Dt⁎+qkt⁎)/qkt−1⁎ and rbt is the real return on nominal debt, which isgiven by rbt=1/(qbt−1Pt).

In the case of Eq. (3), the equivalent of Eq. (4) is written as

Ct + NFAt = WtHt + Dt + r Vxtαt−1 + rktNFAt−1; ð5Þwhere r'xt=[(rkt⁎−rkt), (rrt−rkt)], where rrt=1/qrt−1 is the returnon the non-contingent bond and α't−1=[qkt−1⁎ Sft−1, qrt−1Bt−1].This representation of the budget constraint in each case allows usto solve the portfolio problem for the choice of α, using the procedureof Devereux and Sutherland (2006, 2007).

Representative household z in the home country has a utilityfunction of the form:

Uz = E0X∞t=0

θtC1 − ρzt

1− ρ− χ

1 + μH1 + μ

zt

" #ð6Þ

where ρN0, μN0, χN0, C is consumption and Et is the expectationsoperator conditional on time-t information. θt is the discount factor,which we assume to be endogenous and determined as follows

θt + 1 = θtβ Cztð Þ; θ0 = 1 ð7Þ

where β(Czt)=ωCzt−η.

The budget constraints in each case for the foreign country arewritten analogously, and foreign agents have similar preferences.

Following Schmitt-Grohe and Uribe (2003), the role of θt is toensure a stationary wealth distribution for the linear approximateddynamic model. As is well known, with constant identical timediscount factors in each country, the distribution of world wealth is

3 The model does not formally separate the emerging market economy's holdings offixed income claims on the advanced economy from holdings of international reserves.As shown in Section 2, much of the asset build-up of emerging economies can beattributed to the growth of official reserves. Most of the literature attempting toexplain the large growth in reserves follows the approach we take; i.e. treating thereserve holding decision as done by a dynamic optimizing agent with intertemporalpreferences. In particular, this is the case for Jeanne and Ranciere (2006) and Jeanne(2007), as well as Caballero and Panageas (2004). So long as governments arebenevolent, this distinction should not make much difference. A separate issueconcerns the widespread view that the growth in international reserves came fromforeign exchange rate intervention, in an attempt to maintain undervalued nominalexchange rates. This mechanism would be substantially more difficult to model in ourframework, since we would have to incorporate some type of failure of Ricardianequivalence. The reason is that with full Ricardian equivalence, the official holdings offoreign exchange rate reserves should not impact on the economy's net foreign bondholdings, since the private sector would internalize the present value of assets orliabilities implicit in the official reserve holdings. In addition, in order to explore thismechanism, we might need to introduce some type of price rigidity so that a fixednominal exchange rate could successfully affect an economy's competitiveness. Whileit is likely that official intervention does play a large role in the build-up of nominalclaims of emerging markets, we feel that these complications are enough that they arebest dealt with in further research.

indeterminate in a steady state when financial markets are incom-plete. Allowing for an endogenous time discount factor ensures aunique steady state distribution of wealth. In addition, for ηN0, thefirst-order dynamics in the neighborhood of a steady state displaystrict saddle path properties. The parameter ω allows for structuraldifferences in savings propensities across the two countries. Below, wecalibrate ω (and its foreign counterpart) so that the home country hasa negative NFA in the steady state. We comment in more detail belowon the computation and calibration of steady NFA positions.

3.2. Firms

In each country, competitive firms maximize the present value ofdividends. In the home economy for instance, the firm's objectivefunction is written as

EtX∞i=0

Θt + iDt + i; ð8Þ

where Dt=AtF (Kt, Ht)−WtHt− It−ϕ(It). Thus, dividends are com-prised of output, less wage income, less investment, where we assumethat investment is subject to adjustment costs. The adjustment costfunction satisfies the conditions; ϕ′N0, ϕ″N0, ϕ(I

–)=ϕ'(I

–)=0, where

I–represents the steady state level of investment. Given a level of

investment I, capital accumulation is described by:

Kt + 1 = It + 1− δð ÞKt : ð9Þ

In Eq. (8), the firm uses the stochastic discount factor Θt+ i toevaluate its dividend stream. This will be related to the household'sstochastic intertemporal marginal rate of substitution (SMRS). In theNP and the EB case, Θt+ i is just equal to the home household's SMRS,since the home firm is fully owned by the home household. In the EQcase, Θt+ i is a convex combination of the home and foreign SMRS.4

We assume that the firm's production function is a standard Cobb–Douglas, so that F (Kt, Ht)=Kt

γ Ht1−γ. In addition, At represents a sto-

chastic productivity shock, which is characterized by

logAt = fA logAt−1 + eA;t ; ð10Þ

where 0≤ζA≤1, and εA is an i.i.d. shock symmetrically distributedover the interval [−ε,ε] with Var[εA]=σA

2 .The specification for the foreign economy is analogous. Foreign

firms choose investment and employment to maximize the expectedpresent value of dividends, evaluated at the relevant stochastic dis-count factor.

3.3. The price level

By assumption, only the home country's nominal bonds aretradable internationally. This means that the only relevant pricelevel is that of the home country. In the home economy, the dollarprice of the consumption good is assumed to determined by a simplequantity theory relationship of the form

Mt = XtPtYt : ð11Þwhere M is the nominal money supply in the home country, Ω is a‘velocity’ shock to money demand, and Yt=AtKt

γ Ht1−γ is output in

the home country. This is a short-cut approach to a more involvedspecification incorporating an explicit cash-in-advance constraint onexpenditures.5 For simplicity, we assume Mt grows at a constant rate

4 For the foreign firm, the discount factor in the EB case is assumed to be a weightedaverage of the home and foreign consumers' SMRS.

5 In the case of explicit cash-in-advance constraints, there would also appeardistortionary wedges in the optimality equations for labor and capital. To make Eq. (11)exactly identical to a cash-in-advance economy, it would be necessary to assume that aseparate lump-sum tax financed fiscal policy is used to eliminate these distortions.


m, and the velocity shock Ω is be determined by an autoregressiveprocess of the form

logXt = logXt−1 + eM;t ð12Þ

where εΩ is an i.i.d. shock symmetrically distributed over the interval[−ε,ε] with Var[εΩ]=σΩ

2. This is meant to be a general term whichcaptures shocks to the transactions technology, such as financialinnovation in the banking sector or shocks to the liquidity of thefinancial system. The key feature of this shock is that it generatesuncertainty in the price level. In subsequent discussion, we refer to thisas avelocity shock. In termsof thedeterminationof the optimal portfoliostructure, it has identical effects to a shock to the money supply.

3.4. Optimality conditions

Households in each economy choose consumption, hours worked,saving, and an optimal portfolio of assets under each different financialmarket structure. We state the optimality conditions for the homecountry. Labor supply is characterized by the first order condition:

χΘtHμt = λtWt ð13Þ

In the NP economy, optimal consumption implies:

qrtλt = β Ctð ÞEtλt + 1: ð14Þ

where λt is the Lagrange multiplier associated with the budgetconstraint.

In the EB economy (14) is replaced by the two conditionspertaining to the choice of equity holdings and nominal bonds:

q⁎ktλt = β Ctð ÞEtλt + 1 D⁎t + 1 + q⁎kt + 1

� �; ð15Þ

qbtλt = β Ctð ÞEtλt + 1 = Pt + 1 ð16Þ

Finally, in the EQ economy, the relevant conditions are Eqs.(14)and (15) for non-contingent bonds and foreign equity, while for homeequity the optimality condition is:

qktλt = β Ctð ÞEtλt + 1 Dt + 1 + qkt + 1� �

: ð17Þ

In all cases λt is given by

λt = C−ρt + 1tηωC− 1 + ηð Þ

t

where ςt is the Lagrange multiplier associated with Eq. (7). The first-order condition for the evolution of ςt is given by

1t = Et 1t + 1ωC−ηt + 1 + C1 − ρ

t + 1 = 1− ρð Þ− χH1 + μt + 1 = 1 + μð Þ

h iFirms in each economy choose employment and investment in the

standard fashion.For the home economy, the relevant conditions are:

1− γð ÞAtKγt H

−γt = Wt ; ð18Þ

Θt 1 + / V Itð Þ½ � = EtΘt + 1 γAt + 1Kγ − 1t + 1 H1 − γ

t + 1 + 1− δð Þ 1 + / V It + 1� �� n o

: ð19Þ

3.5. Market clearing conditions

The model is closed by market clearing conditions for goods andasset markets.

Yt + YTt = Ct + CT

t + It + / Itð Þ + ITt + / ITt� �

; ð20Þ

Bt + BTt = 0 ð21Þ

Sft + STft = 1; ð22Þ

Sht + STht = 1; ð23Þ

Bht + BTht = 0: ð24Þ

Bonds are in zero net supply. We normalize so that the total supplyof shares of the firm in each economy is unity. In the NP economy, onlyEqs. (20) and (21) apply, since there is no trade in nominal bonds orequity. In the EB economy, the conditions (20), (22), and (24) apply,while in the EQ economy,(20), (21), (22) and (23) apply.

3.6. The current account and ΔNFA

It is useful to define ΔNFAt≡NFAt−NFAt−1 to be the change inhome net foreign assets. In the EB economy it is simple to show that

ΔNFAt = CAt + r Vxtαt−1

where CAt≡WtHt−Ct+Dt+(rbt−1)NFAt−1 corresponds (approxi-mately) to the conventionally measured current account. Notice thatΔNFAt differs from CAt by the term r'xtαt−1, which represents theunanticipated valuation effect arising from gross asset positions. Asimilar relationship holds in the EQ economy. But in the NP economy,where gross and net asset positions are identical, no unanticipatedvaluation effects exist, so CAt=ΔNFAt by definition.

4. Model solution

In the NP case, Eqs. (1), and (9), (13), (14), (18), (19), along withthe analogous equations for the foreign country, as well as Eqs. (20)and (21) may be solved to determine the path of Bt , Bt⁎, Ct , Ct⁎, It , It⁎,Kt , Kt⁎ , Ht , Ht⁎, Wt , Wt⁎, and qrt. In the EB economy, the conditions (2),and (9), (13), (15), (16), (18), (19), along with the analogousequations for the foreign country, as well as Eqs. (11), (20) (22) and(24) may be solved to determine the path of Bht , Bht⁎ , Sft⁎ , Sft , Ct , Ct⁎, It ,It⁎, Kt , Kt⁎, Ht , Ht⁎, Wt , Wt⁎, Pt , qbt and qkt⁎ . Finally, for the EQ economy,the conditions(3), and (9), (13), (14), (15), (17), (18), (19), along withthe analogous equations for the foreign country, as well as, Eqs. (20),(21), (22) and (23) may be solved to determine the path of Bt , Bt⁎, Sht ,Sht⁎ , Sft⁎, Sft , Ct , Ct⁎, It , It⁎, Kt , Kt⁎, Ht , Ht⁎, Wt , Wt⁎, qkt and qkt⁎ .

The model determines a stochastic distribution of output,consumption, employment, and capital, as well as a time-varyingpath of debt and equity holdings. Of course, as in almost allapplications of stochastic DGE models, it is not possible to obtainthe exact solution of the model in any of these cases. The usualapproach in general equilibrium modelling is to solve by linearapproximation around a steady state. In the NP economy, this methodmay be applied without difficulty, because the only relevantendogenous asset variable is the net foreign asset holding. In the EQcase it is also relatively simple to solve a linear approximation of themodel by exploiting the relationships implied by perfect risk sharing.But in the EB case, it is necessary to solve also for the portfoliocomposition of asset holdings between bonds and equity. To obtainthis portfolio solution for the model, it is necessary to incorporatehigher order aspects of the model approximation, involving thedegree to which each asset is useful in hedging against income risk foreach country.

We solve the model by the approximation methods developed inDevereux and Sutherland (2006, 2007). This involves a two partsolution. First, using a second-order approximation of the portfolioequilibrium conditions, and the equivalent expression for the foreigneconomy, in combination with a first-order approximation of the restof the model, we may solve for the zero-order, or steady-stateportfolio division between equity and debt. This allows us todetermine how the stochastic structure of the model determines

6 For an example of such an outcome, see Durdu et al. (2007).


portfolio allocation, and to characterize the economy's first-orderresponse to stochastic shocks under an optimal portfolio. But we arealso interested in how portfolio holdings themselves respond tostochastic shocks in the economy. To compute this, we followDevereux and Sutherland (2007) in taking a third-order expansionof the portfolio conditions, in combination with a second-orderexpansion of the rest of the model.

4.1. Computing optimal portfolios

Before we analyse the solution of the model in detail, we brieflydescribe the approach to computing optimal portfolio behaviour. Inany two-country DSGE model, there will be a set of portfoliooptimality conditions for the two countries, such as:

Etλt + 1rxt + 1 = 0; Etλ⁎t + 1rxt + 1 = 0; ð25Þ

where rx represents the excess return on the asset portfolio, relative toa reference asset and λ and λ⁎ are the Lagrange multipliers associatedwith the budget constraints in the home and foreign countries. Inaddition, any DSGE model will have a set of equations which may becharacterized as

Et Xt + 1;Xt ; Yt + 1;Yt ; Zt + 1; Zt� �

= 0; ð26Þ

where Xt, Yt, and Zt represent respectively a vector of endogenousstate variables, control variables, and exogenous shock processes.

The solution for Eqs. (25) and (26) will give a vector of realportfolio holdings α(Xt, Zt) for each traded asset. In general, it isdifficult to obtain solutions for portfolios in DSGE models, or even tocharacterize the properties of the solutions. In Devereux and Suther-land (2006, 2007), a simple method is developed for solving for thecharacteristics of α(Xt, Zt), at the zero and first order.

A brief description of the method is as follows. In a static, partialequilibrium environment with one investor, Samuelson (1970) showsthat in order to obtain the properties of the portfolio at the orderN, it isnecessary to approximate the investor's utility function up to the orderN+2. Samuelson's method involves identifying the optimal portfoliofor small shocks. We employ Samuelson's method in the case of adynamic, general equilibrium environment. In our case, the optimalportfolio is approximated as

α Xt ; Ztð Þ≈α X; Z� �

+ αX X; Z� � bxt + αz X; Z

� � bzt ;where X

—, Z—, represent the non-stochastic steady-state values of X and

Z, and x , z represent log deviations from the non-stochastic steady-state. The term α(X

—, Z—) represents the zero-order, or steady state

portfolio, while the αx(X—, Z—)x and αz (X

—, Z—)z terms represent the

first-order components of the portfolio, capturing the way in whichreal portfolio holdings adjust to predictable changes in state variables.Devereux and Sutherland (2006) show that α(X

—, Z—) may be obtained

by a combination of a second-order approximation of Eq. (25), and afirst-order approximation of Eq. (26), where the approximation istaken at the non-stochastic steady-state point. Devereux and Suther-land (2007) show that αx(X

—, Z—) and αz (X

—, Z—) may be obtained by a

third-order approximation of Eq. (25), in combination with a second-order approximation of Eq. (26).

4.2. Computing steady state NFA

As previously noted, the endogeneity of the discount factor in Eq.(6) ensures stationarity in the NP and EQmodels. While this ensures awell-defined steady state wealth distribution across the two coun-tries, it provides no direct guidance regarding the appropriate cali-bration and computation of the steady state NFA position. It istherefore useful to describe our resolution of this problem beforeanalysing our model in detail.

One way to tie down the steady state NFA position is to choosevalues for the parameter ω in Eq. (7), and its foreign counterpart ω⁎,to deliver empirically plausible NFA holdings in the non-stochasticsteady state of the model. The parameters ω and ω⁎ make it possibleto capture structural differences in savings propensities across the twocountries. Thus, for instance, ifω is less thanω⁎ the home country willhave relatively lower steady state consumption, and the home NFAposition will be negative in the non-stochastic steady state. In thisway, a non-zero steady state NFA position is supported and explainedby differences in time preferences between the two countries. Inparticular one could calibrate ω and ω⁎ in our model to yield a non-stochastic steady state NF A position for the home country approxi-mately equal to the current US NFA position (i.e. approximately−20%of GDP).

This approach to determining steady state NFA is not fullysatisfactory however, either from an empirical or theoretical perspec-tive. Empirically, while there may be some grounds to believe that thecurrently observed negative US NFA position (and the correspondingpositive NFA position of developing nations) is partly driven bydifferences in time preferences, it is likely that a substantial part of theNFA position is driven by precautionary savings on the part ofdeveloping countries (see Bernanke, 2005). In theoretical terms, it isunsatisfactory to base the approximation of our model around anexogenously determined steady state level of NFA. In the exactsolution to the model, the distribution of NFAwill be determined bothby differences in time preferences, themenu of assets available for risksharing, and the distribution of country specific risk faced by homeand foreign households6. For given gross positions, differences incountry specific risk give rise to differences in the degree of‘precautionary saving’ among households in the two countries. Butthe menu of available assets also determines the size of the gross assetand liability positions that countries hold. With larger gross assetpositions, differences between countries in time preference or countryspecific risk also give rise to larger net positions, or in other wordslarger NFA.

To capture these effects in the approximate solution to our model,we solve for the stochastic steady state of the second-orderapproximation of the model. This captures the impact of secondmoments of variables on their first moments, or equivalently, howrisk affects the mean levels of endogenous economic variables. Thedifference between the stochastic steady state value for NFA and thevalue in a deterministic steady state in this second-order solutionthus provides an approximate measure for the impact of uncertaintyon NFA in the solution of the exact non-linear stochastic model. Incomputational terms, we follow an iterative procedure which startswith a second-order approximation of the model taken around aninitial guess for the steady state NFA position. The stochastic steadystate of this approximation is used to update the approximation pointand the model is re-solved to yield a new estimate of the stochasticsteady state. The procedure is repeated until the solution for the NFAposition converges. This provides our approximate solution for theNFA position in the stochastic steady state of the exactly solvedmodel.

In the simulations reported below, we set η=0.01 and we chooseω andω so that the benchmark version of the EBmodel yields a homecountry NFA position of −20% of GDP in an approximate stochasticsteady state (computed using the methodology just described). Thevalues of ω andω thus chosen are held constant across the NP, EB andEQ models, and across the other parameter variations reported below,and the approximate stochastic steady state is computed for each case.The steady state NFA position therefore varies endogenously inresponse to differences in risk across the different versions of the

Table 1Model calibration.

Parameter Value Parameter Value

β(C–), β(C

–⁎) 0.96 ζA 0.9

ρ 1 ζA⁎ 0.9µ 1 σA 0.02γ 0.36 σA⁎ 0.05γ⁎ 0.5 σM 0.05δ 0.1 εϕ 0.3η 0.01 ω/ω⁎ NFA�=−0.2Y

Table 2Volatility and correlations in the NP economy.

SD(C) SD(C⁎) cor(C, C⁎) SD(Y) SD(Y⁎) cor(Y, Y⁎)

1.19% 2.58% 0.35 2.32% 5.65% −0.08


model and across the different parameter variations. The resultingvalues of steady state NFA are reported below.

5. Risk sharing under alternative asset market configurations

5.1. Calibration

In order to solve the model, we first need to choose parametervalues. In the absence of a more detailed study of emerging marketeconomies, we choose a set of parameter values guided by previousliterature. Table 1 describes the calibration.

We choose the parameters of β(.) so that the steady-state realinterest rate is 4%.

We assume agents have log utility of consumption. The consump-tion constant elasticity of labor supply is set to unity. The share ofcapital in the production function in the home economy is set at 0.36,as is standard, but noting the lower share of labour in GDP in emergingmarket economies we set this parameter to 0.5 for the foreign country.We set the persistence parameter on the productivity shock equal to0.9 for each country The capital depreciation rate is set at 0.1. Wechoose the volatility of productivity disturbances roughly tomatch thestandard deviation of productivity shocks in the US, and the muchhigher volatility found in emerging markets (see, e.g. Garcia-Ciccoet al., 2007). Hence the standard deviation of home productivityshocks are set at 2%, and the standard deviation of foreign productivityis set at 5%. The standard deviation of velocity shocks is set approx-

Fig. 5. Trade in non-contingent

imately to match the annual standard deviation of money velocity forthe US economy, which is 0.05. We follow previous literature on in-vestment adjustment costs in choosing the elasticity of the ϕ function,εϕ, so that the implied elasticity of Tobin's q to investment is 0.3 (e.g.Bernanke et al., 1999). χ and χ⁎ are chosen so that Y =Y ⁎=1.

5.2. The NP economy

In the absence of any portfolio diversification, the degree of risk-sharing is determined only by intertemporal borrowing and lending.In this sense, the NP model is essentially equivalent to that of Baxterand Crucini (1995). Fig. 5 and Table 2 describe the basic risk-sharingproperties of the model. Fig. 5 illustrates the response of the tradebalance, output, and consumption to shocks to home countryproductivity. Table 2 describes the volatility of consumption andoutput in the NP economy. Both output and consumption volatility arehigher for the foreign economy, given that it experiences a highervariance of productivity shocks, and risk sharing is limited to a non-contingent bond. In Fig. 5, a home productivity shock will initiallygenerate a home country trade account deficit, as both consumptionand investment in the home country rise relative to the foreigncountry. The rise in productivity also leads to a small rise in foreigncountry consumption, as investment falls in the foreign country,increasing foreign residents’ dividend payments for any level ofoutput. As is common in one-good neoclassical models, the homecountry productivity shock causes a rise in home output, but a slightfall in foreign output, since both investment and labor supply fall inthe foreign economy.

Note that, since there is no portfolio diversification in the NPeconomy, the behavior of gross and net foreign assets is equivalent.In addition, since the rate of return on the real bond is not state

bonds (the NP economy).

Table 3The equilibrium portfolio, NFA, volatility and correlations in the EB economy.

qkSf�/K�⁎ SD(C) SD(C⁎) cor(C, C⁎) SD(Y) SD(Y⁎) cor(Y, Y⁎) NFA�/Y�

Benchmark 0.73 1.16% 2.50% 0.50 2.50% 5.75% −0.16 −0.2σM=0.025 1.33 1.18% 2.28% 0.68 2.64% 5.89% −0.22 −0.35σM=0.0 1.84 1.19% 2.03% 0.92 2.78% 6.02% −0.28 −0.50σA=0.01 0.67 0.87% 2.46% 0.51 1.28% 5.73% −0.24 −0.23


contingent, the response of the trade account and ΔNFA is equivalent.That is, there can be no valuation effects of shocks throughmovements in the ex-post return to external assets or liabilities.

The restricted risk sharing offered by the asset menu in the NPeconomy implies a strong incentive for precautionary savings for thedeveloping country. We find that the developing country has a steadystate NFA position of approximately 118% of GDP, which is consider-ably higher than the position implied by the EB model for thebenchmark parameter set (which is calibrated to be 20% of GDP).

5.3. The EB economy

In the EB economy, we have to solve for the portfolio shares ofequity and nominal bonds held by each country. These portfoliopositions will in turn impact on the degree of risk-sharing that isachieved across countries. Following the procedure described inSection 4 above, we first solve for the steady-state portfolio holdings.

Table 3 and Fig. 6 describe the results for the EB economy. Inequilibrium, the foreign economy takes a large positive position inhome currency nominal bonds. That is, Bhb0. At the same time, it sellsequity-FDI to the home country. Since nominal bond returns arepositively correlated with home GDP, and equity returns co-varypositively with foreign GDP, this represents an efficient risk-sharingportfolio allocation. The steady-state portfolio is measured relative tothe steady-state capital stock of the foreign country. Table 3 indicatesthat qk�

Sf /K�⁎=0.73, so that the home country will hold about 73% of

the foreign capital stock in FDI.7

Why does the home country take a positive position in FDI? This ismost easily explained by considering the case where η=0 (i.e. whereconsumers' discount factors are exogenous). In this case the zero-order portfolio represents a solution to the orthogonality condition

Et bCt + 1 − bC⁎t + 1

� �brxt + 1

h i= 0 ð27Þ

where a hat indicates a first-order log-deviation from the approxima-tion point. The motive for portfolio diversification may be obtained bycomputing, from a first-order approximation of the model, the co-variance between relative consumption and the expost excess return,when there is a zero portfolio, i.e. in the absence of any portfoliodiversification. For a zero portfolio, a rise in A, the home countryproductivity, leads to a rise in relative home consumption, but a fall inthe excess return on foreign equity. This is primarily due to fall in thehome country price level, increasing the realised return on the holdingof home currency bonds.8 A rise in A⁎, the foreign productivity shock,leads to a rise in the excess return on foreign equity, since it directlyincreases the dividend payment of the foreign firm, but a fall inrelative home consumption. Thus, on both counts, holding a positive

7 Since the capital output ratio in the foreign economy is about 3.5, this representsan equity holding of about 2.6 times steady-state output. Since qbBh

�+qk Sf�=NFA� and

NFA�=−0.2Y� it follows that home country gross debt is about 2.8 times steady-stateoutput. Note that the model does not incorporate any trading costs or other frictionswhich could potentially reduce the degree of portfolio diversification. The aim is toexplore the maximum degree of cross country risk-sharing that can be achieved in theEB economy relative to a complete markets environment, independent of otherpotential impediments to international financial investment.

8 A rise in home output will lead to a fall in P, as implied by Eq. (11). Since there isone world good and no barriers to trade, PPP will hold at all times and the rise in P isequivalent to an appreciation of the nominal exchange rate.

(negative) position in foreign equity (home bonds) represents anoptimal diversification strategy for home-country residents.

The equilibrium portfolio under the EB economy increases thedegree of risk-sharing considerably relative to the NP economy. Thecross correlation of consumption rises considerably, and consumptionvolatility falls in the foreign country, while consumption volatility inthe home country is essentially unchanged.9

Fig. 6 shows the impact of a shock to home country technology inthe EB economy. The impact on home consumption is less, and that onforeign consumption is greater, than that of the NP economy. Theimpact of the shock on the trade account is now slightly positive, sincehome consumption increases by less as a result of the risk-sharinginherent in the optimal portfolio position.

Fig. 6 shows that the degree of cross-country risk-sharing isintimately tied to ‘valuation effects’, coming from the response of theex-post return on bonds, and the ex-post return on foreign equity.Following a shock to the home country technology, the home pricelevel falls (or equivalently, the exchange rate appreciates). So thereturn on home currency bonds rises. Since the home productivityshock is persistent, the expected rate of return on all assets must rise.This reduces investment in the foreign country, leading to a fall in thereturn on the foreign equity. On both counts, the home country suffersa capital loss on its portfolio, since it has a negative position on its owncurrency bonds, and a positive position in foreign country equity. Thesum of the slight positive movement in the trade account, and thelarge capital loss on the portfolio lead to a sharp deterioration in thehome country ΔNFA. The movement in ΔNFA and the trade accountdiffer due to this valuation effect on the pre-existing portfolio. Hence,net foreign assets fall abruptly, even though the trade account movesalmost not at all. The fall in net foreign assets reduces homeconsumption (and increases foreign consumption) relative to theresponse in the NP economy. The critical point is that this valuationeffect represents an optimal, ex-post, risk-sharing mechanism, giventhe distribution of productivity shocks in each country.

How does the degree of risk sharing depend upon the underlyingdistribution of shocks? Table 3 illustrates the effects of different levelsof volatility of home-country velocity and technology. Lower volatilityof home velocity leads to a much larger (more positive) home FDIposition (and simultaneously a more negative bond position). Areduction in the volatility of velocity implies that the return onnominal bonds is more closely correlated to real shocks and thusbonds become a more useful risk-sharing instrument. This leads tomore consumption risk sharing, i.e. the cross-country correlation ofconsumption increases.

Table 3 shows that lower volatility of home technology leads to asmaller home-country gross asset and liability position. This is because,for a given level of velocity volatility, lower volatility of technologyimplies that the home country nominal bond return is more dominatedby velocity shocks. Hence, the nominal bond becomes a less efficientrisk-sharing instrument. A lower volatility of home country technologytherefore reduces the size of gross portfolio holdings.

The final column of Table 3 reports the steady state NFA positionsimplied by the different parameter variations. As previously ex-plained, we choose values of ω and ω⁎ which imply that the steadystate NFA position of the developed country is −20% of GDP in thebenchmark case. The resulting steady state NFA position is thereforepartly determined by differences in time preferences and partlydetermined by the endogenous responses to economic uncertainty inthe model, including the role of precautionary savings. The absolutesize of the net position is also influenced by the absolute size of grossportfolio positions. Ceteris paribus, for given differences in time

9 Of course, in the case where one country has higher autarky consumptionvolatility, gains from asset trade do not necessarily imply that all countries reduceconsumption volatility, relative to autarky.

10 αFDIt is defined to be the holdings of foreign equity at the end of period t. Thus αFDIt

is a function of the values of the state variables realised at the end of period t. Giventhe notational convention we have adopted for time subscripts, it follows that αFDIt is afunction of Ât, A t, Mt, Ft, K t+1 and Kt+1.

Fig. 6. Trade in home nominal bonds and foreign equity (the EB economy).


preference, the larger is the gross asset and liability position, the largerwill be the net position also. The relative importance of all these forceschanges in the different cases illustrated in Table 3. There is thus nosingle simple explanation for the steady state NFA position in thedifferent cases, except to note that, as the degree of risk sharing isincreases, precautionary savings diminish and the NFA position islargely a result of differences in time preferences.

5.3.1. Capital flowsThe solution for steady-state optimal portfolio holdings is all that is

required toderive the response of the real economy to shocks at the levelof first-order approximation, and therefore characterizes the implica-tions for cross country risk sharing in terms of the second moments ofconsumption. But, as discussed in Section 3, the true portfolio holdingswill in general, be time-varying, moving in response to changes in netforeign assets, as well as predictable changes in productivity and capitalstocks in each country. The dynamics of home country holdings offoreign equity and domestic bonds will be related to movements in thethree underlying shocks in the model; A, A⁎ and M, and the threepredetermined endogenous state variables, NFA, K, andK⁎. FromSection3, we may describe the first-order movement in the home countryholding of FDI, αFDIt=qkt⁎ Sft, in the EB case as

bαFDIt = αFDIt − α≈γ1 bAt + γ2 bA⁎t + γ3 bMt + γ4 bNFAt + γ5 bKt + 1

+ γ6 bK⁎t + 1: ð28Þ

Because portfolio holdings must add up to net wealth, it must alsobe the case that αFDIt+ αBt=NFÂt.10 Hence, from Eq. (28), we mayalso determine the dynamics of real holdings of nominal bonds, giventhat NFÂt is determined by the first-order approximation of the modeldescribed previously.

For the benchmark parameter set the γ coefficients are

γ1 = 0:660; γ2 = 1:267; γ3 = 0:0; γ4 = 0:865;γ5 = 0:549; γ6 = 0:763

The interpretation of the γ coefficients is as follows. A rise in eitherA or A⁎ will lead the home country to increase its positive position inforeign equity, as well as its negative position in home bonds. Asdescribed in Devereux and Sutherland (2007), this is due to the factthat persistent movements in productivity will lead to an increase inthe covariance between relative consumption and excess returns, asdescribed in Eq. (27), generating an increased desire for hedgingrelative consumption risk, which is satisfied by a rise in the size ofgross portfolio positions. The movement in home and foreign capitalstocks has a similar effect. Portfolio holdings are independent of the

11 It is necessary to allow for holdings of real bonds because the two economies areasymmetric - having different shares of capital in production, and thus different sharesof equity returns in total income, in an autarky situation. We could also allow for freeequity trade and trade in the home country nominal bond. In this case, the portfoliooutcome is almost identical to that reported below. That is, agents take large equitypositions, and very small positions in nominal bonds - and the market is complete.Hence, the assumption of no foreign holdings of foreign equity in the EB model isimportant for the results. The rationalization for this assumption has been discussed infootnote 2.12 Thus the home country holds a short position in home equity and the foreigncountry holds a short position in foreign equity.

Table 4Volatility and correlations in the EQ economy.

SD(C) SD(C⁎) cor(C, C⁎) SD(Y) SD(Y⁎) cor(Y, Y⁎)

1.64% 1.40% 0.98 2.64% 6.16% −0.32


dynamics of velocity shocks, since anticipated velocity shocks areneutral in this model. In addition, we find that an increase in netforeign assets, NFÂ, tends to be disproportionally allocated towardsforeign equity relative to home currency nominal bonds.

Fig. 6 illustrates the response of gross assets to the productivityshock. From our previous discussion, we know that net foreign assetsfall. Fig. 6 shows that this fall in net foreign assets is broken down into afall in the gross FDI assets, and a rise in gross nominal debt liabilities.Thus, an optimal response to a positive home productivity shock is toreduce the holdings of foreign equity, and increase gross nominal debt.

Recall that αBt=qBtBt and αFDIt=qkt⁎ Sft. So real gross asset andliability movements, i.e. changes in αFDI t and αBt, may be furtherbroken down into price and volume movements. Changes in αBt cantherefore be broken down into changes in price, qBt, and changes involume, Bt. Likewise, changes in αFDIt can be broken down intochanges in qkt and the changes in Sft. To a first-order approximation thefollowing relationships hold

bα FDIt= qTkSf × bqTkt + bSftbαBt = qBB × bqBt + bBt

ð29Þ

where, for convenience, we define S ft=q�k⁎(Sft−S�f) and Bt=q�B (Bt−B�).

From the discussion above, it follows the rise in A leads to a rise in qBt

(since the anticipated future price level falls) and a fall in qkt⁎. We alsoknow that both bond holdings, αBt, and equity holdings, αFDIt, fall. It issimple to use Eq. (29) to calculate the implied movements in Bt and S ft.These are also plotted in Fig. 6. As an example, consider period 1 inmoredetail. In period 1 the fall in bond holdings is 1.29% (of Y�) whereas bondprices, qBt, rise by 1.23%. Using the fact that qBB

�=−2.76 Eq.(29)implies that Bt=2.10 in period 1, i.e. in volume terms Bt rises. Thechange in equity holdings in period 1 is−2.44% while the equity price,qkt⁎ , falls by 0.16%. Combinedwith the fact that qk⁎Sf=2.56 it follows fromEq. kt(29) that S ft=−2.05. So the fall in equity holdings is accounted forby a combination of a fall in qkt and a fall in S ft, i.e. both the price andvolume of equity holdings fall.

5.3.2. Diversification with real bondsAn important part of the mechanism that determines portfolio

diversification in the EB economy is movement in the home economyprice level. This allows the homenominal bond to act partially as a claimon home output, but on the other hand, exposes the foreign holders ofbonds to price level uncertainty coming from velocity shocks. Howwould the risk sharing potential change if, alternatively, all homenominal bond returns were fixed in real terms (rather than nominal)?This would still allow some potential risk-sharing, because the homecountry would still assume part of the foreign productivity risk byholding foreign equity, while the foreign country residents would hold apositive quantity of non-contingent claims on the home economy. It iseasy to amend our model to the case of real (or indexed) bonds ratherthan nominal bonds. The results indicate the presence of a trade-off. Onthe one hand, if there were no velocity shocks to the price level, thennominal bonds would be more desirable in terms of risk-sharingpotential, since they offer an indirect state contingent claim on homeoutput, whereas the return on real bonds are fixed in output terms. Onthe other hand, if velocity shocks are high enough, then theysubstantially reduce the desirability of foreigners to hold nominalbonds, which in turn, in equilibrium, reduces the size of home equityholdings on the foreign economy. This can eliminate the overall ability ofthe EB economy to sustain risk sharing. As a result, the equilibriumwithreal bonds may offer more overall risk-sharing potential. Note also thatthe EB economy has implications for monetary policy. Take anequilibrium where monetary authorities targeted the domestic pricelevel. If the domestic price level were fixed, the nominal bondwould nolonger act as a partial claim on domestic output. As discussed inSvensson (1989), when nominal bonds allow for risk sharing, price leveltargeting is not necessarily a desirable monetary rule.

5.4. The EQ economy

How does the degree of risk-sharing in the asymmetric case of thelast section compare with a world asset market where there isunrestricted trade in equities? We now focus on the EQ economy,where there is trade in both home and foreign equities and non-contingent bonds. In this case, there is effectively complete markets11.

For the benchmark parameter set, we find the optimal steady-stateportfolio holdings imply that the home country holds foreign equityequivalent to 234% of the foreign capital stock while the foreigncountry holds home equity equivalent to 350% of the home capitalstock.12 Thus each country takes a large positive position in the equityof the other country. In fact, as in Baxter and Jermann (1997), eachcountry holds a larger position in foreign equity than in home equity,since home equity returns and (non-diversifiable) home labor incomeare positively correlated. The implied volatility and correlation ofconsumption and output is shown in Table 4. There is perfect risksharing across countries. But note that the cross-country correlation ofconsumption is not equal to unity because of the effects of en-dogenous discounting.

We find that the steady state NFA position of the home economy inthe EQmodel is−45% of GDP. With complete markets and perfect risksharing there is clearly no role for precautionary savings, so this NFAposition largely reflects the large size of absolute gross positions, incombination with differences in time preferences.

The mechanics of risk-sharing in the EQ case are very similar tothose of the EB case. Fig. 7 illustrates that a rise in home productivityleads to an immediate capital loss on the home portfolio, since thehome country is short (long) in the home (foreign) equity. Withunrestricted trade in equity, it is possible to hold gross equity assetsand liabilities to the extent that these equity valuation effects perfectlyshare consumption risk.

We may also describe capital flows in the EQ model. Fig. 7illustrates that the fall in net foreign assets following a rise in A isaccounted for by a reduction in gross foreign equity assets and a rise inhome equity liabilities. But again, the decomposition into price andvolume effects differs between assets and liabilities. The rise in theprice of home equity automatically increases the liability position ofthe home country, for a given equity holding. Since the rise in theequity price increases gross liabilities more than the equilibriumresponse of home equity liabilities, in the adjustment to the shock, thehome country actually increases its holdings of home equity.

5.5 Discussion

In comparing the three financial structures we may conclude thatthe EB configuration, which can be thought of in a very crude sense asreflecting the portfolio inter-relationship between emerging

Fig. 7. Trade in home and foreign equities and non-contingent bonds (the EQ economy).


economies and advanced economies, can sustain a considerabledegree of cross-country risk-sharing. But the risk-sharing achieved isalways less than that under full unrestricted trade in equity, as in theEQ economy. Moreover, the maximum feasible risk-sharing is limitedby velocity volatility in the home economy. The higher is the volatilityof velocity, the less successful are home-currency nominal bonds insustaining risk-sharing, and the closer is the EB economy to the NPeconomy. Moreover, paradoxically, we find that, for a given degree ofvelocity volatility, a fall in output volatility in the home economy willreduce gross portfolio holdings, since it reduces the efficiency ofnominal home currency bonds in sharing risk.

We have also shown that the implications of optimal portfoliostructure of the gross flows of international capital, and the break-down of portfolio adjustment into price and volume effects may bequite complex, depending on the types of shocks as well as otherdetails of the model.

6. Conclusions

The recent engagement of emerging market economies in theinternational financial system has led to greater optimism withrespect to the ability of these countries to reduce the consumption andincome implications of their high level of country risk. But the con-sequences of financial market integration for international risk-

sharing, at least when financial markets remain incomplete, arecomplicated, and depend on the available menu of assets and the sizeof optimal financial portfolios. Previous literature in this area has beenlimited by the difficulty in incorporating portfolio choice in policy-relevant dynamic general equilibrium environments. This paperrepresents a first step in addressing these limitations, using somerecent theoretical advances in dynamic portfolio choice modelling.Future developments in modelling are required more accurately toaccount for the size and evolution of observed country portfolios. Thiswill likely require a more general model, potentially incorporatingmultiple goods, home bias in consumption and trading costs.

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a portfolio model of capital flows to emerging markets

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